Calculating device



Dec. 8, 1936. H. A. AIKINS 2,063,287 CALCULATING DEV-ICE Original Filed Oct 24, 1932 II II II II II I0 Y 9 V9 INVENTOR.

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Patented Dec. 8, 1936 UNITED STATES PATENT OFFICE Application October 24, 1932, Serial No. 639,178 Renewed May 28, 1936 7 Claims.

This invention relates to calculating devices,

and more particularly calculating devices in which it is desired to visualize the mechanics and logic of the operation. Addition carried on according to the decimal system is in essence a determination of how many tens or multiples of tens and additional units there are in a given group of objects; multiplication is the'determination of how many tens and multiples thereof and additional units there are in so many groups of a given number; and division is a determination of how many groups of a given number are required to make so many tens or multiples and Thus multiplication and division are equatings of groups of ten or multiples thereof with groups of some other number. In accordance with the present invention, a device may be had which not only effects the calculation, but shows both groupings at once and thus visualizes the significance of the performance.

To the accomplishment of the foregoing and related ends, the invention, then, comprises the features hereinafter fully described, and par ticularly pointed out in the claims, the following description and the annexed drawing setting forth in detail certain illustrative embodiments of the invention, these being indicative however, of but a few of the various ways in which the principle of the invention may be employed.

In said annexed drawing:

Fig. 1 is a side elevational view of an embodi-' ment of the invention in position ready for use; Fig. 2 is a similar view with a calculation complete; Fig. 3 is an enlarged transverse sectional view taken on a plane substantially indicated by the line III-III, Fig. 1; Fig. 4 is a front elevational view of a modification; Fig. 5 is an enlarged detail thereof; Fig. 6 is a fragmentary enlarged detail of another modification; Fig. '7 is a fragmentary elevation of another form; Fig. 8 is afragmentary further enlarged sectional detail of the same; and Fig. 9 is a front elevational view of another modification.

In its general aspects, the invention contemplates a flexible cord with counters thereon, and a device with spaced edges or a receiving frame about which the cord is to be wound for exposing groups of the counters. The flexible cord may be a suitably durable string, or wire, capable of being wound and unwound without interfering, kinking, etc. As shown in Fig. 1, such flexible cord 2 may be attached at one end to the device which is to provide the spaced edges, and which comprises the fixed edge 3, extending thence as up-standing arms 4, 5, along which an adjustable edge or bar 6 may be slideably positioned. The frame 3, 4, 5, may be of suitably heavy rod stock to maintain its shape against deformation, and may be notched with indents or recesses I at spaced intervalsalong the arms 4, 5. The adjustable bar 6 may engage by resilient anchorages, such as extension portions 8 which normally spring in to lodge in the notch or recess 1, and which have a thumb lug 9, to be conveniently pried out by insertion of the operator's thumb, whereby to be slideable out of the notch and into the new position selected. While the counters on the cord may be fixed thereto, ordinarily I prefer to have them slideable, and in such case, the cord may be of sufiicient overlength to afford a surplus to take up slack and allowalso free movement of the counters in the act of winding and placement. With counters H) of globular form, or at least a form capable of easy manipulation and separation, and each of uniform diameter along the cord, a definite space-relation will be maintained in terms of' number of counters. If desired, the counters may bear consecutive numbers from one on up to the end of the series, whatever the series chosen may be, and as a further aid in quick visualization and grasping the significance of the process in question, I prefer to distinguish fundamental groups in the series by distinguishing contour form or color. For example, the counters of the entire series may be distinguished by colors, the first ten being green, the next ten being black, the next ten red, the next ten or decade blue, the next ten or decade yellow, and so on. Additionally, in some cases I may distinguish the fifth and sixth or the two middle counters of each group by a further distinctive color, for instance a stripe. In such manner, the respective groups are not only more quickly identifiable, but an assistance in following the operation is had. In the use of colors for distinction, instead of contour conformation, I in general prefer to arrange the colors so as to prevent confusion by users who may happen to be color-blind. For instance, red should not be placed next in series to green, nor red to yellow or brown, nor green toyellow or brown, since such arrangement would quite frequently occasion confusion in cases of the common red-green type of color-blindness. In general, I interpose whites, blacks or blues between the confusing colors, or arrange for a sharp contrast in luminosity perceptible even to the totally color blind.

In the use of the device, for very simple illustration, suppose it is desired to carry out the operation of multiplying four by eight. The adjustable bar or edge on the frame is set a distance equal to the diameter of four counters away from the other bar or edge; the frame is held by one hand (usually the left) in front of the operator, in about the position of a printed card to be read, preferably with the adjustable bar up. The knot attaching the cord to this bar is pushed or kept well over to the left (near the hand which holds the frame), and the counters are made to slide along the cord until they are all crowded together near the frame. Then the cord is grasped three or four inches behind the row of counters (i. e. between the counters and the free end of the cord) by the other hand (say the right), and from time to time throughout the rest of the operation the cord is allowed to slip through the fingers so as to maintain three or four inches of bare cord in addition to the amount of cord covered by the counters between the fingers and the frame. Holding the cord in this way, the right hand moves down behind the frame and up in'front of it in eight successive circles which may be quite continuous and unbroken. In the first swing downward behind the frame all the counters are allowed to slip down the cord toward the moving hand until they fall below the lower edge or bar 3, thus leaving the cord behind the frame quite bare. As the swing is continued the cord touches the bar, then presses against it and continues to do so while the hand moves up in front of the frame (i. e. between the frame and the operator), and the counters again slip downward on the cord, this time away from the moving hand, until the first of them is stopped by the bar and remains pressed against it, and slowly sliding around its rounded surface, until the circular motion of that part of the cord is stopped by the upper bar. The other counters, also acted on by gravity, press down upon the one against the lower bar and are crowded together on the cord until the latter in its continued motion reaches the upper bar, which it' strikes between the fourth and fifth counters (from the bottom) and bends around in such a way as to leave four counters firmly caught between the bars, while the fifth is wedged away and carried around the bar until it finally falls with the remainder of the counters toward the moving hand when the circular motion has brought the latter down far enough behind the frame. In the second and all subsequent swings the operator takes pains to see that the rows of counters are laid on the frame reasonably close together in proper or consecutive order (each a little farther toward the right than the one before it). But inasmuch as gravity takes the counters away from the frame on the downward swing behind it and presses them against it on the upward swing in front, no special care or act or skill is necessary to put all the counters in front where they can be seen and counted, or to have them arranged there in proper sequence. When the eight swings have been completed and eight rows of four counters each have been left on the front of the frame it will be seen that these comprise three complete colored decades and two additional counters (say all the greens, all the blacks, all the reds, and two of the blues), and

thus it is seen that eight times four are thirtytwo. The arrangement of colors on the frame can be studied to show the relations between the rows of four (the multiplicand) and the colored tens at each step of the multiplication; and if the counters are numbered the numbers can be read off. Thus the significance of the whole operation of multiplying becomes clear. For other calculations the adjustable bar 6 is of course set at its appropriate point, depending upon what is to be multiplied; and as readily apparent, the extent of groups may be taken as desired, and with groups, whether in tens, as described foregoing, or twelves or other selected arrangement, the general principle of action remains the same, and by series of twelve similar counters on the cord instead of a series of ten it would show how objects could be counted by the dozen or bought and sold in English shillings and pence without any use of the common scale of ten. As readily apparent also, the various other usages of the device, whether for addition or division, will be understood without further detail mention.

In the form shown in Figs. 4 and 5, the frame comprises a lower bar 3a, and an up-standing end member 4a, with a lower handle extension H. The up-standing frame member 40. is provided with holes or recesses r into which the adjustable upper bar 6a may be seated, frictionally or screw-threadedly, its particular position being determined by the calculation to be made or the desired groupings to be wound off.

In the form of the device shown in Fig. 6, the frame members 42), 5b, are provided with openings or holes, the latter through and through perforations l6, and the former screw-threaded openings H, such that the adjustable bar 6b can be positioned through the selected opening 6 and be screwed tight into the selected opening H, a small knurled thumb portion I8 facilitating such manipulation. It will be understood that the number of openings l6, l1, corresponds to the number of stages or groupings desired.

In some instances, the upper adjustable bar may take the form of a silghtly troughed sheet metal member 60, Figs. '7 and 8, this having perforations so as to be slidable upon the end members 40, 50, being adjustable therealong by engagement of the perforation edge in the notches or recesses 10. The bar 6c may have sufficient resilience to allow a slight compression of its trough by grasping each end with the thumb and fingers, whereby to spring the edge l9 sufficiently to clear the notch 70, and allow movement up or down to the next desired positioning. It will be noticed further, that with such arrangement the trough-like shape of the bar 60 facilitates a positive engagement positioning of the counters.

In the form shown in Fig. 9, the bars 3e, Be, are carried by handle extensions 20, 2|, which are in intertwisting mutual engagement or screw-pitched adjustment, the pitch being related to the diameter of the counter, such that for instance a revolution of one bar will change the spacing by the diameter of one counter, and thus the frame can be set for whatever grouping is desired. The winding of the cord and counters is; as described in the foregoing.

Other modes of applying the principle of the invention may be employed, change being made as regards the details described, provided the features stated in any of the following claims, or the equivalent of such, be employed.

I therefore particularly point out and distinctly claim as my invention:-

1. A calculating apparatus which comprises a flexible cord, a series of counters thereon, a device having spaced edges about which the cord is to be Wound for exposing groups of counters in accordance with the spacing and means whereby the distance between said spaced edges may be varied.

2. A calculating apparatus, Which comprises a flexible cord, counters thereon, a device having a fixed bar and an adjustably spaced bar about which the cord is to be wound for exposing groups of counters in accordance with the spacing.

3. A calculating apparatus, which comprises a flexible cord, counters thereon, a device having a fixed bar with a series of recesses, and an adjustably spaced bar to receive said cord, the latter being insertable in a selected holding recess in said device.

4. A calculating apparatus, which comprises a flexible cord, counters thereon, a device having relatively adjustable spaced bars to receive said cord, and screw threaded means for maintaining the bars in spaced adjusted position.

5. A calculating apparatus, which comprises a flexible cord, counters thereon, a device having a fixed bar with a series of notches, and an adjustably spaced bar about which the cord is to be wound for exposing groups of counters in accordance with the spacing, the latter bar being a trough section, and resiliently engageable with the notches in said device.

6. A calculating apparatus, which comprises a flexible cord, a series of counters thereon, and a cord-receiving device having a fixed bar with upstanding ends carrying a series of recesses and an 'adjustably spaced bar, the latter bar having resilient recess-engaging ends.

7. A calculating apparatus, which comprises a flexible cord, a series of counters thereon, and a cord-receiving device having a fixed bar with upstanding ends carrying a series of recesses, and an adjustably spaced bar with screw-engagement in a selected recess.

HERBERT AUSTIN AIKINS. 

